Finite Group Databasebeta

← #7688368

Subgroups — #7688368

Order 512.

5075 conjugacy classes of subgroups.

The subgroup lattice has 1122 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59875C211yesmaximal, characteristic, complemented
2#59427C212yesmaximal, complemented
3#59425C214yesmaximal, complemented
4#59245C212yesmaximal, complemented
5#59239C214yesmaximal, complemented
6#59134C212yesmaximal, complemented
7#45001C214yesmaximal, complemented
8#43691C218yesmaximal, complemented
9#39159C212yesmaximal, complemented
10#39155C214yesmaximal, complemented
11#38984C212yesmaximal, complemented
12#38983C214yesmaximal, complemented
13#36598C211yesmaximal, characteristic, complemented
14#36579C212yesmaximal, complemented
15#36303C212yesmaximal
16#36274C212yesmaximal, complemented
17#36188C211yesmaximal, characteristic, complemented
18#36177C212yesmaximal, complemented
19D4×C4⋊Q8C211yesmaximal, characteristic, complemented
20#35888C214yesmaximal, complemented
21#34945C211yesmaximal, characteristic, complemented
22C2×#2568C212yesmaximal, complemented
23#34334C212yesmaximal, complemented
24#34191C212yesmaximal, complemented
25C4×D4×Q8C211yesmaximal, characteristic, complemented
26C4×#547C211yesmaximal, characteristic
27C2×#556C2212yes—
28C2×D4×Q8C2212yes—
29C2×D4×Q8C2211yescharacteristic
30C2×#547C2211yescharacteristic
31C22×C4⋊Q8C2212yes—
32C2×C4×#41C2212yes—
33C22×C4×Q8C2212yes—
34#2868C2211yescharacteristic
35#2862C2212yes—
36#2857C2212yes—
37#2857C2212yes—
38#2855C2214yes—
39#2850C2214yes—
40#2810C2214yes—
41#2789C2218yes—
42#2788C2218yes—
43#2783C2218yes—
44#2775C2218yes—
45#2767C2218yes—
46#2762C2218yes—
47#2759C2218yes—
48#2758C2218yes—
49#2745C2218yes—
50#2716C2218yes—
51#2645C2214yes—
52#2643C2218yes—
53#2605C2218yes—
54#2592C2214yes—
55#2588C2218yes—
56#2582C2212yes—
57#2581C2214yes—
58#2573C2214yes—
59#2571C2211yescharacteristic
60#2571C2212yes—
61#2570C2214yes—
62#2568C2214yes—
63#2568C2214yes—
64#2568C2212yes—
65#2568C2212yes—
66#2568C2214yes—
67#2568C2211yescharacteristic
68#2568C2218yes—
69#2568C2212yes—
70#2568C2212yes—
71#2568C2214yes—
72#2568C2212yes—
73#2551C2212yes—
74#2551C2212yes—
75#2547C2212yes—
76#2547C2212yes—
77#2547C2211yescharacteristic
78#2546C2212yes—
79#2545C2214yes—
80#2538C2211yescharacteristic
81#2533C2218yes—
82#2532C2218yes—
83#2514C2212yes—
84#2514C2214yes—
85#2514C2214yes—
86#2514C2214yes—
87#2514C2214yes—
88#2514C2214yes—
89#2511C2214yes—
90#2511C2214yes—
91#2510C2218yes—
92#2509C2214yes—
93#2503C2214yes—
94#2499C2214yes—
95#2497C2214yes—
96#2496C2214yes—
97#2496C2214yes—
98#2495C2214yes—
99#2494C2212yes—
100#2493C2218yes—
101#2493C2218yes—
102#2493C2218yes—
103#2492C2214yes—
104#2492C2214yes—
105#2492C2214yes—
106#2488C2218yes—
107#2488C2218yes—
108#2481C2218yes—
109#2481C2218yes—
110#2469C2218yes—
111#2451C2214yes—
112#2450C2218yes—
113#2447C2212yes—
114#2446C2214yes—
115#2446C2214yes—
116#2440C2214yes—
117#2440C2214yes—
118#2439C2214yes—
119#2439C2214yes—
120#2438C2218yes—
121#2436C2214yes—
122#2434C2214yes—
123#2421C2212yes—
124#2421C2214yes—
125#2417C2214yes—
126#2409C2214yes—
127#2401C2214yes—
128C2×#400C2218yes—
129#2369C2214yes—
130#2368C2218yes—
131#2365C2212yes—
132#2365C2212yes—
133#2365C2211yescharacteristic
134#2365C2212yes—
135#2365C2212yes—
136#2365C2211yescharacteristic
137#2362C2214yes—
138#2362C2212yes—
139#2361C2212yes—
140#2360C2214yes—
141#2360C2214yes—
142#2360C2212yes—
143#2359C2214yes—
144#2356C2214yes—
145#2355C2212yes—
146#2355C2212yes—
147#2355C2212yes—
148#2355C2212yes—
149#2355C2212yes—
150#2354C2211yescharacteristic
151#2352C2214yes—
152#2352C2214yes—
153Q8×C4⋊C4C2211yescharacteristic
154#2349C2214yes—
155D4×C4⋊C4C2212yes—
156D4×C4⋊C4C2212yes—
157D4×C4⋊C4C2211yescharacteristic
158D4×C4⋊C4C2212yes—
159D4×C4⋊C4C2211yescharacteristic
160#2346C2214yes—
161#2344C2212yes—
162#2343C2218yes—
163Q8×C22⋊C4C2214yes—
164Q8×C22⋊C4C2212yes—
165#2339C2212yes—
166#2339C2214yes—
167#2339C2214yes—
168#2331C2214yes—
169#2329C2218yes—
170#2320C2214yes—
171#2318C2218yes—
172C4×C4⋊Q8C2211yescharacteristic
173C4×C4⋊Q8C2212yes—
174C4×C4⋊Q8C2212yes—
175C4×C4⋊Q8C2211yescharacteristic
176C4×C4⋊Q8C2211yescharacteristic
177C4×#124C2212yes—
178C4×C22⋊Q8C2214yes—
179C4×C22⋊Q8C2214yes—
180C4×C22⋊Q8C2212yes—
181C4×C22⋊Q8C2212yes—
182C4×C22⋊Q8C2212yes—
183C4×#123C2214yes—
184C4×#121C2212yes—
185#2295C2212yes—
186C2×#391C2214yes—
187C2×#391C2214yes—
188C2×#391C2214yes—
189#2285C2212yes—
190#2283C2214yes—
191#2283C2212yes—
192C2×#382C2214yes—
193#2275C2214yes—
194C42×Q8C2211yescharacteristic
195C42×D4C2211yescharacteristic
196C42×D4C2212yes—
197C42×D4C2211yescharacteristic
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2312yes—
200C23×Q8C2312yes—
201C23×Q8C2314yes—
202#556—48no—
203D4×Q8—28no—
204D4×Q8—216no—
205#547—28no—
206C2×C4⋊Q8—48no—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2314yes—
216C2×C4⋊Q8C2314yes—
217C2×C4⋊Q8C2312yes—
218C2×#126C2318yes—
219C2×#124C2314yes—
220C2×#124C2312yes—
221C2×#123C2314yes—
222C2×C22⋊Q8C2318yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2314yes—
229C2×#121C2312yes—
230C4×#41—216no—
231C2×C4×Q8—48no—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2314yes—
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2314yes—
244C2×C4×Q8C2314yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2314yes—
248C2×C4×D4C2312yes—
249C2×C4×D4C2312yes—
250C2×C4×D4C2312yes—
251C2×C4×D4C2314yes—
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×#117C2314yes—
258C2×#117C2312yes—
259C2×#117C2314yes—
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2314yes—
263C22×C4⋊C4C2312yes—
264C22×C4⋊C4C2314yes—
265C22×C4⋊C4C2314yes—
266C22×C42C2314yes—
267C22×C42C2312yes—
268C22×C42C2312yes—
269C22×C42C2314yes—
270#401C2318yes—
271#401C2318yes—
272#401C2314yes—
273#400C2314yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2318yes—
283#400C2314yes—
284#400C2318yes—
285#400C2318yes—
286#400C2318yes—
287#400C2314yes—
288#400C2318yes—
289#400C2318yes—
290#400C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#397C2314yes—
295#397C2318yes—
296#397C2314yes—
297#397C2318yes—
298#397C2314yes—
299#397C2318yes—
300#396C2314yes—
301#396C2318yes—
302#396C2318yes—
303#395C2318yes—
304#395C2318yes—
305#395C2318yes—
306#393C2318yes—
307#393C2318yes—
308#393C2318yes—
309#391C2314yes—
310#391C2312yes—
311#391C2312yes—
312#391C2314yes—
313#391C2312yes—
314#391C2314yes—
315#391C2312yes—
316#391C2314yes—
317#391C2312yes—
318#391C2312yes—
319#391C2314yes—
320#391C2314yes—
321#391C2318yes—
322#391C2318yes—
323#391C2314yes—
324#391C2314yes—
325#391C2314yes—
326#391C2318yes—
327#391C2314yes—
328#391C2314yes—
329#391C2318yes—
330#391C2318yes—
331#391C2318yes—
332#391C2314yes—
333#391C2314yes—
334#391C2314yes—
335#391C2314yes—
336#391C2314yes—
337#391C2318yes—
338#391C2318yes—
339#391C2312yes—
340#391C2312yes—
341#391C2314yes—
342#391C2312yes—
343#391C2314yes—
344#390C2312yes—
345#390C2312yes—
346#389C2312yes—
347#389C2314yes—
348#389C2312yes—
349#389C2312yes—
350#389C2314yes—
351#389C2312yes—
352#389C2312yes—
353#389C2312yes—
354#389C2312yes—
355#389C2314yes—
356#389C2312yes—
357#389C2314yes—
358#389C2312yes—
359#389C2312yes—
360#389C2314yes—
361#389C2312yes—
362#389C2312yes—
363#389C2318yes—
364#389C2312yes—
365#389C2314yes—
366#389C2314yes—
367#389C2314yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#389C2312yes—
372#388C2314yes—
373#388C2314yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2314yes—
380#388C2314yes—
381#388C2314yes—
382#388C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2314yes—
386#387C2314yes—
387#387C2314yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2314yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2314yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2314yes—
406#387C2314yes—
407#387C2314yes—
408#387C2314yes—
409#386C2318yes—
410#386C2318yes—
411#386C2318yes—
412#386C2314yes—
413#386C2314yes—
414#386C2318yes—
415#385C2314yes—
416#385C2314yes—
417#385C2318yes—
418#385C2314yes—
419#385C2318yes—
420#385C2314yes—
421#385C2314yes—
422#385C2318yes—
423#385C2318yes—
424#385C2314yes—
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#384C2312yes—
429#384C2312yes—
430#384C2312yes—
431#384C2312yes—
432#384C2312yes—
433#383C2314yes—
434#383C2318yes—
435#383C2318yes—
436#383C2318yes—
437#382C2312yes—
438#382C2314yes—
439#382C2318yes—
440#382C2318yes—
441#382C2314yes—
442#382C2314yes—
443#382C2314yes—
444#382C2314yes—
445#382C2314yes—
446#382C2314yes—
447#382C2312yes—
448#382C2312yes—
449#381C2314yes—
450#381C2318yes—
451#381C2318yes—
452#381C2314yes—
453#380C2314yes—
454#380C2318yes—
455#380C2314yes—
456#380C2314yes—
457#380C2312yes—
458#380C2312yes—
459#380C2312yes—
460#380C2314yes—
461#380C2314yes—
462#380C2314yes—
463#380C2314yes—
464#380C2312yes—
465#380C2312yes—
466#380C2312yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2318yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2311yescharacteristic
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2312yes—
502C4×C22⋊C4C2312yes—
503C4×C22⋊C4C2318yes—
504C4×C22⋊C4C2314yes—
505C4×C22⋊C4C2318yes—
506C4×C22⋊C4C2314yes—
507C4×C22⋊C4C2312yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2318yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2312yes—
517#376C2314yes—
518#376C2318yes—
519C2×#95C2318yes—
520C2×#95C2318yes—
521C2×#95C2314yes—
522C2×#95C2318yes—
523C2×#95C2318yes—
524C43C2311yescharacteristic
525C43C2312yes—
526C2×#41—28no—
527C2×#41—28no—
528C2×#41—28no—
529C22×Q8—28no—
530C22×Q8—28no—
531C22×Q8—216no—
532C22×Q8—44no—
533C22×Q8—48no—
534C22×Q8—48no—
535C22×Q8C2412yes—
536C22×Q8C2414yes—
537C22×Q8C2412yes—
538C22×Q8C2412yes—
539C22×Q8C2414yes—
540C22×Q8C2411yescharacteristic
541C22×Q8C2418yes—
542C22×D4C2411yescharacteristic
543C22×D4C2414yes—
544C22×D4C2411yescharacteristic
545C23×C4C2414yes—
546C23×C4C2412yes—
547C23×C4C2412yes—
548C23×C4C2412yes—
549C23×C4C2414yes—
550C23×C4C2412yes—
551C23×C4C2412yes—
552C23×C4C2418yes—
553C23×C4C2414yes—
554C23×C4C2414yes—
555C23×C4C2412yes—
556C4⋊Q8—28no—
557C4⋊Q8—216no—
558C4⋊Q8—24no—
559C4⋊Q8—24no—
560C4⋊Q8—28no—
561C4⋊Q8—24no—
562C4⋊Q8—28no—
563C4⋊Q8—48no—
564C4⋊Q8—48no—
565C4⋊Q8—48no—
566C4⋊Q8—44no—
567#126—416no—
568#124—44no—
569#124—48no—
570#123—216no—
571C22⋊Q8—28no—
572C22⋊Q8—28no—
573C22⋊Q8—216no—
574C22⋊Q8—28no—
575C22⋊Q8—216no—
576C22⋊Q8—232no—
577C22⋊Q8—48no—
578#121—28no—
579C4×Q8—24no—
580C4×Q8—28no—
581C4×Q8—28no—
582C4×Q8—24no—
583C4×Q8—28no—
584C4×Q8—24no—
585C4×Q8—28no—
586C4×Q8—48no—
587C4×Q8—48no—
588C4×Q8—44no—
589C4×Q8—44no—
590C4×Q8—48no—
591C4×Q8—48no—
592C4×D4—28no—
593C4×D4—28no—
594C4×D4—216no—
595C4×D4—24no—
596C4×D4—28no—
597C4×D4—216no—
598C4×D4—216no—
599C4×D4—24no—
600C4×D4—24no—
601C4×D4—42no—
602C4×D4#4118yes—
603C4×D4#4118yes—
604#117—28no—
605#117—216no—
606#117—48no—
607C2×C4⋊C4—28no—
608C2×C4⋊C4—44no—
609C2×C4⋊C4—44no—
610C2×C4⋊C4—48no—
611C2×C4⋊C4—48no—
612C2×C4⋊C4—48no—
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2418yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2412yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2412yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2412yes—
682C2×C22⋊C4C2412yes—
683C2×C42—216no—
684C2×C42—28no—
685C2×C42—28no—
686C2×C42—48no—
687C2×C42C2414yes—
688C2×C42C2412yes—
689C2×C42C2412yes—
690C2×C42C2414yes—
691C2×C42C2412yes—
692C2×C42C2414yes—
693C2×C42C2414yes—
694C2×C42C2411yescharacteristic
695C2×C42C2412yes—
696C2×C42C2411yescharacteristic
697C2×C42C2414yes—
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2411yescharacteristic
704C2×C42C2412yes—
705C2×C42C2412yes—
706C2×C42C2418yes—
707C2×C42C2414yes—
708C2×C42C2414yes—
709C2×C42C2418yes—
710C2×C42C2411yescharacteristic
711C2×C42C2412yes—
712C2×C42C2418yes—
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716#95C2414yes—
717#95C2412yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2418yes—
722#95C2418yes—
723#95C2418yes—
724#95C2418yes—
725#95C2414yes—
726#95C2414yes—
727#95C2418yes—
728#95C2414yes—
729#95C2418yes—
730#95C2418yes—
731#95C2418yes—
732#95C2418yes—
733#95C2418yes—
734#95C2418yes—
735#95C2418yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2418yes—
742#95C2412yes—
743#95C2412yes—
744#95C2412yes—
745#95C2412yes—
746#95C2414yes—
747#95C2414yes—
748#95C2412yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2412yes—
754#95C2412yes—
755#95C2412yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2418yes—
760#95C2418yes—
761#95C2414yes—
762#95C2414yes—
763#95C2418yes—
764#95C2414yes—
765#95C2418yes—
766#95C2418yes—
767#95C2418yes—
768C24C2512yes—
769C24C2512yes—
770#41—432no—
771C2×Q8—22no—
772C2×Q8—24no—
773C2×Q8—24no—
774C2×Q8—28no—
775C2×Q8—28no—
776C2×Q8—24no—
777C2×Q8—24no—
778C2×Q8—216no—
779C2×Q8—22no—
780C2×Q8—24no—
781C2×Q8—28no—
782C2×Q8—24no—
783C2×Q8—28no—
784C2×Q8—24no—
785C2×Q8—24no—
786C2×Q8—28no—
787C2×Q8—24no—
788C2×Q8—44no—
789C2×Q8—48no—
790C2×Q8—48no—
791C2×Q8—432no—
792C2×Q8—832no—
793C2×Q82−1+414yes—
794C2×D4—28no—
795C2×D4—28no—
796C2×D4—28no—
797C2×D4—22no—
798C2×D4—22no—
799C2×D4—22no—
800C2×D4C2×#4114yes—
801C2×D4C2×#4114yes—
802C2×D42−1+414yes—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—28no—
808C22×C4—28no—
809C22×C4—28no—
810C22×C4—24no—
811C22×C4—28no—
812C22×C4—28no—
813C22×C4—216no—
814C22×C4—28no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—28no—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—44no—
825C22×C4—42no—
826C22×C4—44no—
827C22×C4—48no—
828C22×C4—44no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—48no—
834C22×C4C2×#4118yes—
835C22×C4C2×#4118yes—
836C22×C4C2512yes—
837C22×C4C2514yes—
838C22×C4C2512yes—
839C22×C4C2512yes—
840C22×C4C2511yescharacteristic
841C22×C4C2512yes—
842C22×C4C2514yes—
843C22×C4C2514yes—
844C22×C4C2514yes—
845C22×C4C2514yes—
846C22×C4C2514yes—
847C22×C4C2512yes—
848C22×C4C2512yes—
849C22×C4C2512yes—
850C22×C4C2518yes—
851C22×C4C2511yescharacteristic
852C22×C4C2512yes—
853C22×C4C2512yes—
854C22×C4C2511yescharacteristic
855C22×C4C2511yescharacteristic
856C22×C4C2512yes—
857C22×C4C2511yescharacteristic
858C22×C4C2511yescharacteristic
859C22×C4C2511yescharacteristic
860C4⋊C4—22no—
861C4⋊C4—24no—
862C4⋊C4—28no—
863C4⋊C4—24no—
864C4⋊C4—28no—
865C4⋊C4—28no—
866C4⋊C4—24no—
867C4⋊C4—28no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—22no—
871C4⋊C4—28no—
872C4⋊C4—28no—
873C4⋊C4—216no—
874C4⋊C4—24no—
875C4⋊C4—28no—
876C4⋊C4—24no—
877C4⋊C4—24no—
878C4⋊C4—22no—
879C4⋊C4—24no—
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—28no—
883C4⋊C4—28no—
884C4⋊C4—28no—
885C4⋊C4—22no—
886C4⋊C4—24no—
887C4⋊C4—22no—
888C4⋊C4—24no—
889C4⋊C4—22no—
890C4⋊C4—24no—
891C4⋊C4—28no—
892C4⋊C4—22no—
893C4⋊C4—24no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—48no—
899C4⋊C4—48no—
900C4⋊C4—42no—
901C4⋊C4—42no—
902C4⋊C4—42no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—48no—
906C4⋊C4—48no—
907C4⋊C4—44no—
908C4⋊C4—44no—
909C4⋊C4C2×#4114yes—
910C4⋊C4C2×#4114yes—
911C22⋊C4—28no—
912C22⋊C4—216no—
913C22⋊C4—28no—
914C22⋊C4—28no—
915C22⋊C4—24no—
916C22⋊C4—28no—
917C22⋊C4—24no—
918C22⋊C4—28no—
919C22⋊C4—24no—
920C22⋊C4—28no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—48no—
924C22⋊C4—42no—
925C22⋊C4—48no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4C2×#4118yes—
929C22⋊C4C2×#4118yes—
930C42—24no—
931C42—28no—
932C42—24no—
933C42—24no—
934C42—28no—
935C42—28no—
936C42—24no—
937C42—28no—
938C42—24no—
939C42—24no—
940C42—24no—
941C42—24no—
942C42—28no—
943C42—22no—
944C42—24no—
945C42—24no—
946C42—22no—
947C42—22no—
948C42—24no—
949C42—44no—
950C42—44no—
951C42—41no—
952C42—42no—
953C42—48no—
954C42—48no—
955C42—48no—
956C42C2×#4114yes—
957C42C2×#4114yes—
958C42H(5,𝔽2)14yes—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23C22×#4114yes—
971C23C22×#4114yes—
972C23C2×2−1+414yes—
973C23C2611yescharacteristic
974Q8—28no—
975Q8—416no—
976Q8—48no—
977Q8—416no—
978Q8—48no—
979Q8—48no—
980Q8—816no—
981D4—416no—
982D4—44no—
983D4#556116yescomplemented
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—22no—
991C2×C4—21no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—216no—
997C2×C4—216no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—24no—
1001C2×C4—22no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—22no—
1005C2×C4—24no—
1006C2×C4—22no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—28no—
1010C2×C4—22no—
1011C2×C4—24no—
1012C2×C4—22no—
1013C2×C4—24no—
1014C2×C4—22no—
1015C2×C4—28no—
1016C2×C4—24no—
1017C2×C4—22no—
1018C2×C4—21no—
1019C2×C4—22no—
1020C2×C4—21no—
1021C2×C4—22no—
1022C2×C4—24no—
1023C2×C4—22no—
1024C2×C4—24no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—21no—
1032C2×C4—24no—
1033C2×C4—28no—
1034C2×C4—24no—
1035C2×C4—22no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—48no—
1044C2×C4—416no—
1045C2×C4—416no—
1046C2×C4—48no—
1047C2×C4—48no—
1048C2×C4—84no—
1049C2×C4—88no—
1050C2×C4—88no—
1051C2×C4—816no—
1052C2×C4C22×#4114yes—
1053C2×C4C22×#4112yes—
1054C2×C4C22×#4112yes—
1055C2×C4C22×#4114yes—
1056C2×C4C22×#4112yes—
1057C2×C4C22×#4112yes—
1058C2×C4C22×#4112yes—
1059C2×C4C22×#4112yes—
1060C2×C4C2×H(5,𝔽2)12yes—
1061C2×C4C2×H(5,𝔽2)12yes—
1062C2×C4C2×H(5,𝔽2)12yes—
1063C2×C4C2×2−1+414yes—
1064C2×C4C2×2−1+412yes—
1065C2×C4C2×2−1+412yes—
1066C2×C4#58512yes—
1067C22—24no—
1068C22—24no—
1069C22—24no—
1070C22—24no—
1071C22—24no—
1072C22—24no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22C2×#55618yes—
1081C22C23×#4111yescharacteristic
1082C22C23×#4111yescharacteristic
1083C22C22×H(5,𝔽2)11yescharacteristic
1084C22C22×2−1+411yescharacteristic
1085C22C22×2−1+411yescharacteristic
1086C22C2×#58511yescharacteristic
1087C222−1+611yescharacteristic
1088C4—22no—
1089C4—22no—
1090C4—24no—
1091C4—24no—
1092C4—24no—
1093C4—22no—
1094C4—44no—
1095C4—42no—
1096C4—44no—
1097C4—42no—
1098C4—42no—
1099C4—44no—
1100C4—42no—
1101C4—41no—
1102C4—44no—
1103C4—48no—
1104C4—42no—
1105C4—44no—
1106C4—42no—
1107C4—42no—
1108C4—44no—
1109C4C2×#55614yes—
1110C4#351414yes—
1111C4#352014yes—
1112C2—28no—
1113C2—82no—
1114C2C22×#55611yescharacteristic
1115C2C2×#352011yescharacteristic
1116C2C2×#351411yescharacteristic
1117C2#6294211yescharacteristic
1118C2#6300111yescharacteristic
1119C2#6300911yescharacteristic
1120C2#6303211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#547C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #59875C2semidirect
2. #59427C2semidirect
3. #59425C2semidirect
4. #59245C2semidirect
5. #59239C2semidirect
6. #59134C2semidirect
7. #45001C2semidirect
8. #43691C2semidirect
9. #39159C2semidirect
10. #39155C2semidirect
11. #38984C2semidirect
12. #38983C2semidirect
13. #36598C2semidirect
14. #36579C2semidirect
16. #36274C2semidirect
17. #36188C2semidirect
18. #36177C2semidirect
19. D4×C4⋊Q8C2semidirect
20. #35888C2semidirect
21. #34945C2semidirect
22. C2×#2568C2semidirect
23. #34334C2semidirect
24. #34191C2semidirect
25. C4×D4×Q8C2semidirect
983. D4#556semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#598752
#594272
#594252
#592452
#592392
#591342
#450012
#436912
#391592
#391552
#389842
#389832
#365982
#365792
#363032
#362742
#361882
#361772
D4×C4⋊Q82
#358882
#349452
C2×#25682
#343342
#341912
C4×D4×Q82
C4×#5472